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(B) The given system of linear equations is:$x + y + z = 2$$2x + y - z = 3$$3x + 2y + kz = 4$$A$ system of linear equations has a unique solution if a

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equal to $R - \{0\}$

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(B) The given system of linear equations is:$x + y + z = 2$$2x + y - z = 3$$3x + 2y + kz = 4$$A$ system of linear equations has a unique solution if and only if the determinant of the coefficient matrix is non-zero.Let $D$ be the determinant of the coefficient matrix:$D = \begin{vmatrix} 1 & 1 & 1 \ 2 & 1 & -1 \ 3 & 2 & k \end{vmatrix}$Expanding along the first row:$D = 1(1 \cdot k - (-1) \cdot 2) - 1(2 \cdot k - (-1) \cdot 3) + 1(2 \cdot 2 - 1 \cdot 3)$$D = 1(k + 2) - 1(2k + 3) + 1(4 - 3)$$D = k + 2 - 2k - 3 + 1$$D = -k$For a unique solution,$D 
eq 0$,which implies $-k 
eq 0$,or $k 
eq 0$.Therefore,$S = R - \{0\}$.

Let $S$ be the set of all real values of $k$ for which the system of linear equations $x + y + z = 2$,$2x + y - z = 3$,and $3x + 2y + kz = 4$ has a unique solution. Then $S$ is

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